Nuprl Lemma : fpf-normalize_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[g:x:A fp-> B[x]]. (fpf-normalize(eq;g) ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-normalize: fpf-normalize(eq;g),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
fpf-normalize: fpf-normalize(eq;g),
pi2: snd(t),
pi1: fst(t),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
list-subtype,
reduce_wf,
l_member_wf,
fpf_wf,
fpf-join_wf,
fpf-single_wf,
fpf-empty_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesisEquality,
setEquality,
cumulativity,
because_Cache,
hypothesis,
lambdaEquality,
applyEquality,
lambdaFormation,
setElimination,
rename,
instantiate,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[g:x:A fp-> B[x]].
(fpf-normalize(eq;g) \mmember{} x:A fp-> B[x])
Date html generated:
2018_05_21-PM-09_32_12
Last ObjectModification:
2018_02_09-AM-10_26_56
Theory : finite!partial!functions
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